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- W4381894997 abstract "We characterise the sensitivity of several additive tensor decompositions with respect to perturbations of the original tensor. These decompositions include canonical polyadic decompositions, block term decompositions, and sums of tree tensor networks. Our main result shows that the condition number of all these decompositions is invariant under Tucker compression. This result can dramatically speed up the computation of the condition number in practical applications. We give the example of an $265times 371times 7$ tensor of rank $3$ from a food science application whose condition number was computed in $6.9$ milliseconds by exploiting our new theorem, representing a speedup of four orders of magnitude over the previous state of the art." @default.
- W4381894997 created "2023-06-25" @default.
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- W4381894997 date "2021-06-24" @default.
- W4381894997 modified "2023-09-27" @default.
- W4381894997 title "The condition number of many tensor decompositions is invariant under Tucker compression" @default.
- W4381894997 doi "https://doi.org/10.48550/arxiv.2106.13034" @default.
- W4381894997 hasPublicationYear "2021" @default.
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